The fatal encounter in Columbus, Ohio, between a white officer and a black teenager last year quickly polarized the public.

A grand jury in Columbus, Ohio, declined on Friday to indict a white police officer who fatally shot a 13-year-old black boy who was brandishing a BB gun, finding that the officer’s actions were justified, city officials and the police said.

The officer, Bryan Mason, had chased Tyre King into an alley on Sept. 14 and when the teenager pulled the BB gun from his waistband, the officer opened fire, striking Tyre multiple times, the authorities said.

Mr. Mason, a nine-year veteran of the Columbus Police Department at the time, had fatally shot a man in 2012; his superiors cleared him of any wrongdoing in that episode, but placed him on administrative leave after the September killing.

The shooting quickly polarized the public, as people rallied behind either the officer or the boy. Officials in state’s capital found themselves pleading for patience, acutely aware of the unrest that has sometimes followed police shootings that have claimed the lives of black men. Some had drawn parallels between the shooting of Tyre and the 2014 shooting death of Tamir Rice, 12, who was playing with a pellet gun in a park in Cleveland.

“I am grateful for the patience of the community in awaiting the results of the grand jury investigation into the police-involved shooting of Tyre King,” Mayor Andrew J. Ginther said in a statement on Friday. “The death of a 13-year-old under any circumstances is tragic. I am committed to continuing to work with all residents and the police to break the cycle of violence, build trust and give hope.”

Sean Walton, a lawyer representing the King family, said they were not surprised by the grand jury’s decision, calling the process flawed. He said the family had called for an independent investigation into the shooting and believes the Columbus Police Department and county prosecutor’s office should have stepped aside.

The Columbus Police Department did not release a statement Friday, but the department confirmed that the grand jury had decided not to file charges against the officer.

In its own statement, the Columbus City Council called the decision “a sad and unfortunate reminder that a child has died in our community.”

“While we are grateful for the grand jury’s service and for the community’s patience awaiting these results,” the statement said, “the council is also deeply reflective on how we must aggressively strive to end violence in our community and continue to improve the relationship between the people of Columbus and the criminal justice system.”

After the shooting, the authorities said officers had responded to a report of an armed robbery in the Olde Towne East neighborhood in central Columbus.

They saw three males who matched descriptions they had been given. Two fled and officers chased them into an alley, where Tyre pulled what appeared to be a gun from his waistband, the police said. Mr. Mason shot him multiple times.

At a news conference the next day, public officials bemoaned society’s “obsession with guns” and the problems the culture creates.

Kimberley Jacobs, the police chief, held up a photograph of a BB gun of the kind found in the alley near Tyre to show how similar it looked to the firearms used by the Columbus police.

“Why is it,” Mayor Ginther asked, “that a 13-year-old would have nearly an exact replica of a police firearm on him in our neighborhoods?”